Pattern formation in a cross-diffusive ratio-dependent predator-prey model
type: Item
instance of: scholarly article
title: Pattern formation in a cross-diffusive ratio-dependent predator-prey model
zbMATH Open document ID: 1254.92080
DOI: 10.1155/2012/814069
author: Xinze Lian
author: Yanhong Yue
author: Hailing Wang
published in: Discrete Dynamics in Nature and Society
publication date: 2012-12-18T00:00:00Z
review text: Summary: We present a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatial distribution of the species with self- and cross-diffusion in a Holling-III ratio-dependent predator-prey model. The diffusion instability of the positive equilibrium of the model with Neumann boundary conditions is discussed. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- and cross-diffusion in the model and find that the model dynamics exhibits a cross-diffusion controlled formation growth to spots, stripes, and spiral wave pattern replication, which show that reaction-diffusion model is useful to reveal the spatial predation dynamics in the real world.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 37N25
zbMATH DE Number: 6116524
zbMATH Keywords: evolutionary process
zbMATH Keywords: Holling-III ratio-dependent predator-prey model
zbMATH Keywords: diffusion instability
zbMATH Keywords: positive equilibrium
zbMATH Keywords: Neumann boundary conditions
Wikidata QID: Q58700772
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/814069
OpenAlex ID: W2071038982
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description: scientific article; zbMATH DE number 6116524